Accurately estimating the arterial input function for dynamic contrast-enhanced MRI is challenging. An arterial input function is typically determined from signal magnitude changes related to a contrast agent, often leading to underestimation of peak concentrations. Alternatively, signal phase recovers the accurate peak concentration for straight vessels but suffers from high noise. A recent method proposed to fit the signal in the complex plane by combining the advantages of the previous 2 methods. The purpose of this work is to refine this complex-based method to determine the venous output function (VOF), an arterial input function surrogate, from the superior sagittal sinus. We propose a state-of-the-art complex-based method that includes direct compensation for blood inflow and signal phase correction accounting for the curvature of the superior sagittal sinus, generally assumed collinear with B0 . We compared the magnitude-, phase-, and complex-based VOF determination methods against various simulated biases as well as for 29 brain metastases patients. Angulation of the superior sagittal sinus relative to B0 varied widely within patients, and its effect on the signal phase caused an underestimation of peak concentrations of up to 65%. Correction significantly increased the VOF peak concentration for the phase- and complex-based VOFs in the cohort. The phase-based method recovered accurate peak concentrations but lacked precision in the tail of the VOF. Our complex-based VOF completely recovered the effect of inflow and resulted in a high-peak concentration with limited noise. The new complex-based method resulted in high-quality VOF robust against superior sagittal sinus curvature and variations in patient positioning.
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